Given a trapezoid whose bases are 25 and 4, sides are 20 and 13. Find the area of the trapezoid.

To find the area of the trapezoid, we find its height.

The height is a leg in two right-angled triangles.

In these triangles, the hypotenuses are the lateral sides of the trapezium, the second legs are two segments, the sum of the lengths of which is 25 – 4 = 21. Let’s introduce a variable.

Let one of these segments (legs) be equal to x. The second is then equal to (21 – x).

Let’s equate the squares of the height in two triangles.

400 – x ^ 2 = 169 – (21 – x) ^ 2;

400 – x ^ 2 = 169 – x ^ 2 – 441 + 42 * x;

42 * x = 672;

x = 16;

The height of the trapezoid is:

h = (400 – 256) ^ (1/2) = 12.

S = (a + b) * h / 2 = (25 + 4) * 12/2 = 29 * 6 = 174 cm².